A minimum problem with free boundary for a degenerate quasilinear operator
type: Item
instance of: scholarly article
title: A minimum problem with free boundary for a degenerate quasilinear operator
zbMATH Open document ID: 1068.35187
author: D. Danielli
author: Arshak Petrosyan
published in: Calculus of Variations and Partial Differential Equations
publication date: 2005-05-12T00:00:00Z
review text: The authors prove \(C^{1,\alpha}\) regularity (near flat points) of the free boundary \(\partial\{u>0\}\cap\Omega\) in the Alt-Caffarelli type minimum problem for the \(p\)-Laplace operator: \[ J(u) = \int_{\Omega} (|\nabla u|^{p} + \lambda^{p}\chi_{\{u>0\}}) \,dx \to \min \quad (1<p<\infty). \]
reviewed by: Gheorghe Aniculăesei
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 49J25
Mathematics Subject Classification ID: 35J40
zbMATH DE Number: 2167610
zbMATH Keywords: regularity of the free boundary
zbMATH Keywords: Alt-Caffarelli type minimum problem
zbMATH Keywords: \(p\)-Laplace operator
MaRDI profile type: Publication
full work available at URL: s00526-004-0294-5
OpenAlex ID: W2065818691
cites work: Q3895957
cites work: Q3217048
cites work: Q3480628
cites work: Q4431139
cites work: Q5565773
cites work: Q5187597
cites work: Q4693180
cites work: Existence of classical solutions to a free boundary problem for the p-Laplace operator: (I) the exterior convex case
cites work: Existence of classical solutions to a free boundary problem for the p-Laplace operator: (II) the interior convex case
cites work: Regularity in elliptic free boundary problems. I
cites work: Electrochemical and Electro-Discharge Machining with a Threshold Current
cites work: Q4354419
cites work: On harnack type inequalities and their application to quasilinear elliptic equations
DOI: 10.1007/S00526-004-0294-5
Recommended article: An optimization problem with free boundary governed by a degenerate quasilinear operator.
Recommended article: A Minimum Problem with Free Boundary for the p(x)−Laplace Operator
Recommended article: A free boundary problem for degenerate quasilinear parabolic equations
Recommended article: A free boundary problem for quasilinear degenerate parabolic equations with general degeneracy
Recommended article: Q3336116
Recommended article: Q4306350
Recommended article: Partial regularity for a minimum problem with free boundary
Recommended article: On the minimal solution for quasilinear degenerate elliptic equation and its blow-up
Recommended article: Q3217048
Recommended article: Q3505226
description: scientific article; zbMATH DE number 2167610